Graphene, a two-dimensional sp2-bonded carbon material, has attracted enormous attention due to its excellent electrical, optical and mechanical properties. Recently developed chemical vapor deposition (CVD) methods could produce large-size and uniform polycrystalline graphene films, limited to gas carbon sources, metal catalyst substrates and degraded properties induced by grain boundaries. Meanwhile, pristine monolayer graphene exhibits a standard ambipolar behavior with a zero neutrality point in field-effect transistors (FETs), limiting its future electronic applications. This thesis starts with the investigation of CVD synthesis of pristine and N-doped graphene with controlled thickness using solid carbon sources on metal catalyst substrates (chapter 1), and then discusses the direct growth of bilayer graphene on insulating substrates, including SiO2, h-BN, Si3N4 and Al2O3, without needing further transfer-process (chapter 2). Chapter 3 discusses the synthesis of high-quality graphene single crystals and hexagonal onion-ring-like graphene domains, and also explores the basic growth mechanism of graphene on Cu substrates. To extend graphene’s potential applications, both vertical and planar graphene-carbon nanotube hybrids are fabricated using CVD method and their interesting properties are investigated (chapter 4). Chapter 5 discusses how to use chemical methods to modulate graphene’s electronic behaviors.